{
  "id": 403,
  "curve_key": "229898380672672426460231416567271287514506324256243293825:-3489605340566857343692483516433671868477398134546859113338091213450627489091307980225",
  "ainvs": [
    "1",
    "0",
    "0",
    "-4789549597347342217921487845151485156552215088671735288",
    "4038895070100529332977411476954657751699524878306148134823129956225541669799702592"
  ],
  "rank_lower_bound": 28,
  "torsion": [],
  "naive_height": 389.33387291677536,
  "faltings_height": 30.220962766415294,
  "conductor": "23041381240412411159163335278781148219756014215360760109370073705697070765442268382401335882318018176926510969767537593177464755040274350",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "29",
    "47",
    "5076671",
    "16143317537697055815553",
    "14500332007970721183436484998398890113459",
    "506635894750112623868634415118765751634240595748702020977"
  ],
  "discriminant": "-15315564775743859773341691289544645120730310762127768915894882508509352445128944124435441714677299462641137372755597315156825505771232278317103481761930549022720000",
  "regulator": "20740304673472845962849215040060774.20396559799586898592951377474738348070256530816221888161347",
  "points": [
    [
      "1419451495537511168684583312",
      "10016636136282285835078838529466974857064"
    ],
    [
      "1292140875431703451802599632",
      "2741696599900168568705766212407537728264"
    ],
    [
      "-1554127539571468469351952528",
      "87913380492337621277952909907301690306184"
    ],
    [
      "1397958835686337759990146672",
      "8678556074583426665448039541184765320584"
    ],
    [
      "1890138070783235545861300392",
      "41698126460034390763348625554299939764424"
    ],
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      "1276927435871250956150229552",
      "2252496318802875130984125648714648599304"
    ],
    [
      "1217640884954401260543942432",
      "3504011368921423189906245824679832351704"
    ],
    [
      "1202874839383604410442991252",
      "4256224887588367893909620787164335591704"
    ],
    [
      "1724087135177671081546340292",
      "30101538707170661239481514422736376344984"
    ],
    [
      "1252832940868607213371207632",
      "2196381457007702314449378309397226964264"
    ],
    [
      "1342918522827768584938031472",
      "5364696161567427886286699934055105394184"
    ],
    [
      "-1968110703356380069775016048",
      "76432069985520801134007772286352685216104"
    ],
    [
      "1186623113932211878168758192",
      "5134048983724854708597634990994257566024"
    ],
    [
      "1246645161819603976729700172",
      "2338290308192325124454271360011026845084"
    ],
    [
      "409944476705728968197334912",
      "46307004547414160530881672265476470592264"
    ],
    [
      "1319128590833893794585362412",
      "4034753450891939075667566276312453322264"
    ],
    [
      "1273264904321123077970197272",
      "2179724916324025019958356503780580579784"
    ],
    [
      "1186696906354756081579279512",
      "5129986505942008589202952547315553538464"
    ],
    [
      "1242947307908468956781739432",
      "2447237983284829504997402614270782654864"
    ],
    [
      "1278669687560602602599205552",
      "2294171880161698309278818529944665923144"
    ],
    [
      "1094909451213329591541975408",
      "10362366528276628104240321013380668257800"
    ],
    [
      "1193773363028132974541505732",
      "4743269166135887844505620610174208876964"
    ],
    [
      "1326288578262716370649729062",
      "4423420861494276123455035681945813451124"
    ],
    [
      "1236406574312796280548185712",
      "2675947459623539614255135459247126649864"
    ],
    [
      "-107183062476078148811179248",
      "67461265348457412006093827698026366113544"
    ],
    [
      "1456689479851038650097837252",
      "12370222742162239949637704552167747191204"
    ],
    [
      "1012511438842683902742601662",
      "15080689613131735052862433148397828962574"
    ],
    [
      "-1606532526745840653615624288",
      "87103888361989004911611532588079598044424"
    ]
  ],
  "submitter": "NDElkies",
  "commentary": "Noam D. Elkies and Zev Klagsbrun, January 2026.  The cubic field generated by the x-coordinate of a 2-torsion point has a class group of 2-rank at least 26, the highest known for a cubic number field.",
  "created_at": "2026-08-28 17:01:42",
  "updated_at": "2026-08-28 20:23:57"
}